Consider two firms $($A and B$)$ engaging in Cournot Competition. Both firms face an inverse market demand curve P$($Q$)=700-5$Q$,$ where Q$=$qA$+$qB$.$ The marginal revenue curve for firm A is MRA$=700-10$qA$-5$qB and the marginal revenue curve for firm B is MRB$=700-10$qB$-5$qA$.$ The firms have identical cost functions, with constant marginal cost MC$=20.$

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A$)$ Determine the profit function for firm A and firm B$.$

B$)$ Solve for the best$-$response functions of both firms.

C$)$ Determine the equilibrium quantities both firms will supply, and the corresponding market price.

D$)$ Suppose both firms could collude. Determine the equilibrium price and quantity produced by both firms $($assume both firms split the quantity supplied to the market equally$).$

E$)$ Find the level of dead$-$weight loss associated with parts C$)$ and D$).$ Which equilibrium has a larger amount of dead$-$weight loss? Why?